Finite Group Databasebeta

← #11703582

Subgroups — #11703582

Order 768.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3503C211yesmaximal, characteristic, complemented
2#87043C212yesmaximal, complemented
3#87040C212yesmaximal, complemented
4#87023C212yesmaximal, complemented
5#87016C212yesmaximal, complemented
6#86933C216yesmaximal, complemented
7#86924C216yesmaximal, complemented
8#86748C216yesmaximal, complemented
9D4×#239C216yesmaximal, complemented
10#86597C216yesmaximal, complemented
11#86582C216yesmaximal, complemented
12#86261C213yesmaximal, complemented
13#86257C213yesmaximal, complemented
14#86205C213yesmaximal, complemented
15C2×#5725C213yesmaximal, complemented
16#85900C212yesmaximal, complemented
17#85886C212yesmaximal, complemented
18#85846C211yesmaximal, characteristic, complemented
19C4×D3×#41C211yesmaximal, characteristic, complemented
20#62800—31nomaximal, Sylow
21C2×#1009C2212yes—
22C2×D3×#41C2211yescharacteristic
23C22×#239C2216yescomplemented
24C3×Q82C2212yescomplemented
25C3×#557C2212yescomplemented
26C3×#554C2216yescomplemented
27C3×D4×Q8C2216yescomplemented
28C3×#544C2216yescomplemented
29C3×#533C2213yescomplemented
30C2×C3×C4⋊Q8C2213yescomplemented
31C3×#520C2212yes—
32C3×C4×#41C2211yescharacteristic
33Dic3×#41C2211yescharacteristic
34#5817C22112yescomplemented
35C2×#947C2216yescomplemented
36#5734C22112yescomplemented
37#5734C2216yescomplemented
38#5733C22112yescomplemented
39#5733C22112yescomplemented
40#5732C2216yescomplemented
41#5730C2216yescomplemented
42#5728C2213yescomplemented
43#5728C2211yescharacteristic, complemented
44#5726C22112yescomplemented
45#5726C2216yescomplemented
46#5725C22112yescomplemented
47#5725C2216yescomplemented
48#5725C2216yescomplemented
49#5725C2216yescomplemented
50#5725C2216yescomplemented
51#5725C2213yescomplemented
52#5725C2216yescomplemented
53#5725C2216yescomplemented
54#5725C2216yescomplemented
55#5725C2213yescomplemented
56#5697C22112yescomplemented
57#5697C22112yescomplemented
58#5695C22112yescomplemented
59#5695C22112yescomplemented
60#5691C2216yescomplemented
61#5691C22112yescomplemented
62#5691C2216yescomplemented
63#5644C22124yescomplemented
64#5637C22124yescomplemented
65#5630C22124yescomplemented
66#5630C22112yescomplemented
67#5630C22112yescomplemented
68#5627C22124yescomplemented
69#5627C2216yescomplemented
70#5627C2216yescomplemented
71#5624C2216yescomplemented
72#5624C2216yescomplemented
73#5585C2216yescomplemented
74#5585C2216yescomplemented
75#5580C2216yescomplemented
76#5580C2216yescomplemented
77#5577C2212yescomplemented
78#5577C2214yescomplemented
79#5577C2216yescomplemented
80#5577C2212yescomplemented
81#5577C2216yescomplemented
82#5576C2214yescomplemented
83#5574C2214yescomplemented
84C4×#239C2211yescharacteristic, complemented
85C4×#239C2214yescomplemented
86C4×#239C2216yescomplemented
87C4×#239C2211yescharacteristic, complemented
88C4×#239C2216yescomplemented
89C4×D3×Q8C2211yescharacteristic, complemented
90C4×D3×Q8C2211yescharacteristic, complemented
91#5554C22112yescomplemented
92D4×D12C2216yescomplemented
93D4×D12C2216yescomplemented
94D4×D12C22112yescomplemented
95#5545C22112yescomplemented
96C4×D3×D4C2213yescomplemented
97C4×D3×D4C2213yescomplemented
98C4×D3×D4C22112yescomplemented
99C4×#237C2213yescomplemented
100C4×#237C2213yescomplemented
101#5525C2216yescomplemented
102#5525C2216yescomplemented
103#5524C2216yescomplemented
104#5522C2213yescomplemented
105#5522C2216yescomplemented
106#5521C2216yescomplemented
107D3×#117C2213yescomplemented
108#5514C22112yescomplemented
109#5510C2216yescomplemented
110C2×#895C2216yescomplemented
111C2×#895C2216yescomplemented
112#5504C2216yescomplemented
113C2×#893C2216yescomplemented
114C2×#893C2216yescomplemented
115#5477C2213yescomplemented
116C2×#874C2213yescomplemented
117C4×#235C2213yescomplemented
118C2×C42×D3C2213yescomplemented
119#3522—32no—
120#3519—36no—
121#3517—32no—
122#3514—36no—
123#3511—33no—
124#3508—33no—
125#3503D311yescharacteristic, complemented
126#3498—31no—
127#3494—36no—
128#3488—32no—
129#3483—32no—
130#3481—36no—
131#3480—32no—
132D4×#41—36no—
133#3460—36no—
134#3444—33no—
135C2×#532—33no—
136C4×H(5,𝔽2)—32no—
137C2×C4×#41—31no—
138C2×C3×#41C2311yescharacteristic
139C22×C3×Q8C2316yes—
140#1009—216no—
141D3×#41—28no—
142C2×#239—424no—
143C2×#239C2316yes—
144C2×#239C2311yescharacteristic
145C2×#239C2314yes—
146C2×#239C23112yes—
147C2×#239C23112yes—
148C2×#239C23112yes—
149C2×#239C2316yes—
150C2×D3×Q8C2311yescharacteristic
151C2×#237C2313yes—
152C2×D3×D4C2313yes—
153C2×D3×D4C23112yes—
154C2×#235C2313yes—
155C2×#235C2316yes—
156C22×D12C2316yes—
157C22×D12C2316yes—
158C22×D12C23112yes—
159C22×D12C2316yes—
160C22×C4×D3C2313yes—
161C22×C4×D3C2313yes—
162C22×C4×D3C23112yes—
163C22×C4×D3C2313yes—
164C3×C4⋊Q8C2316yes—
165C3×C4⋊Q8C23112yes—
166C3×C4⋊Q8C2313yes—
167C3×C4⋊Q8C2311yescharacteristic
168C3×C4⋊Q8C2316yes—
169C3×C4⋊Q8C2316yes—
170C3×#125C2316yes—
171C3×#125C23112yes—
172C3×C22⋊Q8C23124yes—
173C3×C22⋊Q8C2316yes—
174C3×C22⋊Q8C2316yes—
175C3×C4×Q8C2311yescharacteristic
176C3×C4×Q8C2314yes—
177C3×C4×Q8C2316yes—
178C3×C4×Q8C2311yescharacteristic
179C3×C4×Q8C2316yes—
180C3×C4×D4C2313yes—
181C3×C4×D4C2313yes—
182C3×C4×D4C23112yes—
183C3×#117C2313yes—
184C3×#117C2316yes—
185C2×C3×C4⋊C4C2316yes—
186C2×C3×C4⋊C4C2316yes—
187C2×C3×C42C2313yes—
188#947C23112yes—
189#947C23112yes—
190#947C23124yes—
191#947C2316yes—
192#947C23112yes—
193#947C2316yes—
194#946C23124yes—
195#946C2316yes—
196#946C2312yes—
197Q8×Dic3C2316yes—
198Q8×Dic3C2312yes—
199Q8×Dic3C2311yescharacteristic
200Q8×Dic3C2311yescharacteristic
201D4×Dic3C2313yes—
202D4×Dic3C2313yes—
203#930C23124yes—
204#930C2316yes—
205#930C2316yes—
206C4×#67C23124yes—
207C4×#67C2316yes—
208C4×#67C2316yes—
209C2×(C2×D3)⋊C4C23112yes—
210C2×(C2×D3)⋊C4C23112yes—
211#926C2313yes—
212C2×C4×Dic3C2313yes—
213C2×C4×Dic3C2313yes—
214C2×C4×Dic3C2313yes—
215#898C23112yes—
216#898C23124yes—
217#898C23112yes—
218#897C2312yes—
219#897C2316yes—
220#897C23112yes—
221#895C23112yes—
222#895C23124yes—
223#895C23112yes—
224#895C2316yes—
225#895C2316yes—
226#895C23112yes—
227#895C23124yes—
228#895C23112yes—
229#895C23112yes—
230#895C23112yes—
231#895C23112yes—
232#895C2316yes—
233#895C23112yes—
234#895C23112yes—
235#895C2316yes—
236#894C23124yes—
237#894C23124yes—
238#894C23112yes—
239#894C23112yes—
240#894C23124yes—
241#893C23112yes—
242#893C23112yes—
243#893C23112yes—
244#893C2316yes—
245#893C2316yes—
246#893C23112yes—
247#893C23112yes—
248#893C2313yes—
249#893C23112yes—
250#893C23112yes—
251#893C2313yes—
252#893C2316yes—
253#893C23112yes—
254#893C2316yes—
255#892C23112yes—
256#892C23112yes—
257#892C2313yes—
258#892C23112yes—
259#892C2316yes—
260#892C2312yes—
261#892C2313yes—
262D3×C4⋊C4C2313yes—
263D3×C4⋊C4C23112yes—
264D3×C4⋊C4C2313yes—
265#890C2316yes—
266#890C2312yes—
267#887C2313yes—
268#887C2312yes—
269#887C2316yes—
270#887C2313yes—
271#886C23112yes—
272#882C23124yes—
273#882C23124yes—
274#882C23112yes—
275#67⋊C4C2316yes—
276#67⋊C4C23112yes—
277#67⋊C4C2316yes—
278#67⋊C4C23112yes—
279D3×C22⋊C4C23124yes—
280D3×C22⋊C4C2316yes—
281#877C2316yes—
282#875C2316yes—
283#875C23112yes—
284#874C2316yes—
285#874C23112yes—
286#874C2313yes—
287#874C2316yes—
288#874C2316yes—
289C4×D12C23112yes—
290C4×D12C23112yes—
291C4×D12C23112yes—
292C4×D12C23112yes—
293C4×D12C2313yes—
294C4×D12C2316yes—
295C4×D12C2313yes—
296C4×D12C2316yes—
297#872C2316yes—
298#872C23112yes—
299C42×D3C2313yes—
300C42×D3C2313yes—
301C42×D3C23112yes—
302C42×D3C2311yescharacteristic
303C42×D3C2313yes—
304C42×D3C2313yes—
305C42×D3C2313yes—
306C42×D3C2313yes—
307C42×D3C2313yes—
308#869C2311yescharacteristic
309C4×Dic6C2313yes—
310C4×Dic6C2313yes—
311C2×H(5,𝔽2)—32no—
312C22×#41—31no—
313C22×#41—36no—
314#559—36no—
315#559—36no—
316Q82C2×D312yescomplemented
317#557C2×D312yescomplemented
318#556—36no—
319#555—312no—
320#555—36no—
321#554—36no—
322#554C2×D316yescomplemented
323#553—312no—
324#553—312no—
325#553—312no—
326#551—324no—
327#550—36no—
328#550—32no—
329#550—34no—
330#550—32no—
331#550—36no—
332D4×Q8C2×D316yescomplemented
333#548—312no—
334#548—34no—
335#547—312no—
336#547—36no—
337#546—324no—
338#546—312no—
339#546—312no—
340#546—312no—
341D42—312no—
342D42—36no—
343D42—36no—
344#544C2×D316yescomplemented
345#542—312no—
346#542—312no—
347#540—312no—
348#540—312no—
349#538—324no—
350#537—36no—
351#535—36no—
352#535—36no—
353#533—31no—
354#533—33no—
355#533C2×D313yescomplemented
356#532—33no—
357#532—36no—
358#532—36no—
359#532—36no—
360#532—36no—
361#532—36no—
362#532—36no—
363#532—36no—
364#532—33no—
365#532—312no—
366#532—33no—
367C2×C4⋊Q8C2×D313yescomplemented
368C2×#127—33no—
369#529—36no—
370#529—36no—
371#529—312no—
372#529—36no—
373#529—36no—
374#529—36no—
375#529—36no—
376C2×#124—36no—
377#525—36no—
378#525—36no—
379#525—324no—
380#525—36no—
381C2×#121—36no—
382C2×#121—36no—
383#520—34no—
384#520—36no—
385#520C2×D312yes—
386#518—312no—
387#518—36no—
388C4×#41—31no—
389C4×#41—31no—
390C4×#41—31no—
391C4×#41—34no—
392C4×#41—36no—
393C4×#41—36no—
394C4×#41—33no—
395C4×#41—33no—
396C4×#41—33no—
397C4×#41—36no—
398C4×#41—33no—
399C4×#41C2×D311yescharacteristic
400C2×C4×Q8—31no—
401C2×C4×Q8—31no—
402C2×C4×D4—33no—
403C2×C4×D4—33no—
404C2×C4×D4—312no—
405C2×C4×D4—36no—
406C2×C4×D4—36no—
407C2×#117—33no—
408C22×C42—33no—
409C23×D3C2413yes—
410C23×D3C24112yes—
411C3×#41#4118yescomplemented
412C2×C3×Q8—412no—
413C2×C3×Q8C2412yes—
414C2×C3×Q8C2416yes—
415C2×C3×Q8C24112yes—
416C2×C3×Q8C2411yescharacteristic
417C2×C3×D4C2413yes—
418C22×C3×C4C2413yes—
419C22×C3×C4C2413yes—
420C22×C3×C4C24112yes—
421C22×C3×C4C2413yes—
422C2×#67C2416yes—
423C2×#67C24112yes—
424C22×Dic3C2413yes—
425C22×Dic3C2413yes—
426C22×Dic3C2413yes—
427#239—24no—
428#239—216no—
429#239—224no—
430#239—424no—
431#239—424no—
432#239—424no—
433#239—412no—
434D3×Q8—24no—
435#237—212no—
436D3×D4—212no—
437D3×D4—248no—
438#235—212no—
439#235—224no—
440C2×D12—224no—
441C2×D12—412no—
442C2×D12—412no—
443C2×D12—424no—
444C2×D12C2413yes—
445C2×D12C24112yes—
446C2×D12C2416yes—
447C2×D12C2416yes—
448C2×D12C24112yes—
449C2×D12C2416yes—
450C2×D12C24112yes—
451C2×D12C24112yes—
452C2×D12C24112yes—
453C2×D12C24124yes—
454C2×C4×D3—212no—
455C2×C4×D3—212no—
456C2×C4×D3—424no—
457C2×C4×D3—46no—
458C2×C4×D3C2411yescharacteristic
459C2×C4×D3C2411yescharacteristic
460C2×C4×D3C2413yes—
461C2×C4×D3C2413yes—
462C2×C4×D3C2413yes—
463C2×C4×D3C2413yes—
464C2×C4×D3C2413yes—
465C2×C4×D3C2413yes—
466C2×C4×D3C2413yes—
467C2×C4×D3C24112yes—
468C2×C4×D3C24112yes—
469C2×C4×D3C2413yes—
470C2×C4×D3C2413yes—
471C2×C4×D3C24112yes—
472C2×C4×D3C24124yes—
473C2×C4×D3C2411yescharacteristic
474C2×Dic6C2413yes—
475C2×Dic6C2412yes—
476C3×C4⋊C4C2413yes—
477C3×C4⋊C4C2413yes—
478C3×C4⋊C4C2416yes—
479C3×C4⋊C4C2412yes—
480C3×C4⋊C4C2416yes—
481C3×C4⋊C4C2412yes—
482C3×C4⋊C4C24112yes—
483C3×C4⋊C4C24112yes—
484C3×C4⋊C4C24112yes—
485C3×C4⋊C4C24112yes—
486C3×C22⋊C4C2416yes—
487C3×C22⋊C4C24112yes—
488C3×C42C2413yes—
489C3×C42C2413yes—
490C3×C42C2411yescharacteristic
491C3×C42C2413yes—
492C3×C42C24112yes—
493#217C2416yes—
494(C2×D3)⋊C4C24112yes—
495(C2×D3)⋊C4C2416yes—
496(C2×D3)⋊C4C2416yes—
497(C2×D3)⋊C4C24112yes—
498(C2×D3)⋊C4C2414yes—
499(C2×D3)⋊C4C24112yes—
500(C2×D3)⋊C4C24112yes—
501(C2×D3)⋊C4C24112yes—
502(C2×D3)⋊C4C24124yes—
503(C2×D3)⋊C4C24112yes—
504(C2×D3)⋊C4C24112yes—
505(C2×D3)⋊C4C24124yes—
506C4⋊Dic3C2413yes—
507C4⋊Dic3C2413yes—
508C4⋊Dic3C2412yes—
509C4⋊Dic3C2412yes—
510C4⋊Dic3C2414yes—
511C4⋊Dic3C24112yes—
512Dic3⋊C4C2416yes—
513Dic3⋊C4C2416yes—
514Dic3⋊C4C2414yes—
515Dic3⋊C4C24112yes—
516C4×Dic3C2413yes—
517C4×Dic3C2413yes—
518C4×Dic3C2413yes—
519C4×Dic3C2411yescharacteristic
520C4×Dic3C2411yescharacteristic
521C4×Dic3C2411yescharacteristic
522C4×Dic3C2414yes—
523C4×Dic3C2413yes—
524C4×Dic3C2413yes—
525C4×Dic3C2413yes—
526C4×Dic3C2413yes—
527C4×Dic3C2413yes—
528C4×Dic3C2413yes—
529C4×Dic3C24112yes—
530H(5,𝔽2)—616no—
531C2×#41—31no—
532C2×#41—34no—
533C2×#41—36no—
534C2×#41—36no—
535C2×#41—312no—
536C2×#41—312no—
537C2×#41—312no—
538C2×#41—33no—
539C2×#41—33no—
540C2×#41—36no—
541C2×#41—68no—
542C2×#41—1224no—
543C2×#41C22×D311yescharacteristic
544C22×Q8—31no—
545C22×Q8C22×D316yes—
546C22×D4—33no—
547C22×D4—312no—
548C22×D4—36no—
549C22×D4—36no—
550C22×D4—312no—
551C22×D4—36no—
552C23×C4—33no—
553C23×C4—33no—
554C23×C4—312no—
555C23×C4—33no—
556C4⋊Q8—31no—
557C4⋊Q8C22×D313yes—
558C4⋊Q8C22×D316yes—
559C4⋊Q8C22×D316yes—
560C4⋊Q8C22×D316yes—
561C4⋊Q8C22×D311yescharacteristic
562C4⋊Q8C22×D3112yes—
563#127—33no—
564#127—36no—
565#127—36no—
566#127—36no—
567#127—312no—
568#126—312no—
569#126—312no—
570#126—324no—
571#125—32no—
572#125—36no—
573#125C22×D316yes—
574#125C22×D3112yes—
575#124—36no—
576#124—312no—
577#124—312no—
578#124—312no—
579#124—36no—
580#124—324no—
581#124—36no—
582#124—312no—
583#123—312no—
584#123—312no—
585#123—324no—
586#123—324no—
587#123—324no—
588#123—312no—
589C22⋊Q8—32no—
590C22⋊Q8—36no—
591C22⋊Q8—324no—
592C22⋊Q8—32no—
593C22⋊Q8—36no—
594C22⋊Q8—312no—
595C22⋊Q8C22×D316yes—
596C22⋊Q8C22×D316yes—
597C22⋊Q8C22×D3124yes—
598#121—36no—
599#121—36no—
600#121—324no—
601#121—36no—
602#121—36no—
603#121—312no—
604#121—312no—
605#121—312no—
606#121—312no—
607#121—312no—
608#121—312no—
609#121—36no—
610#121—36no—
611#121—324no—
612#121—312no—
613#121—312no—
614#121—312no—
615#121—324no—
616#120—312no—
617#120—324no—
618#120—324no—
619C4×Q8—31no—
620C4×Q8—31no—
621C4×Q8—32no—
622C4×Q8—36no—
623C4×Q8—33no—
624C4×Q8—33no—
625C4×Q8—32no—
626C4×Q8—36no—
627C4×Q8—33no—
628C4×Q8—33no—
629C4×Q8C22×D311yescharacteristic
630C4×Q8C22×D311yescharacteristic
631C4×Q8C22×D314yes—
632C4×Q8C22×D316yes—
633C4×Q8C22×D316yes—
634C4×D4—33no—
635C4×D4—33no—
636C4×D4—36no—
637C4×D4—36no—
638C4×D4—324no—
639C4×D4—312no—
640C4×D4—36no—
641C4×D4—36no—
642C4×D4—33no—
643C4×D4—33no—
644C4×D4—312no—
645C4×D4—312no—
646C4×D4—312no—
647C4×D4—312no—
648C4×D4—312no—
649C4×D4—36no—
650C4×D4—312no—
651C4×D4—312no—
652C4×D4—36no—
653C4×D4—312no—
654C4×D4—36no—
655C4×D4—36no—
656C4×D4—312no—
657C4×D4—33no—
658C4×D4—33no—
659C4×D4—312no—
660C4×D4—312no—
661C4×D4—312no—
662C4×D4—312no—
663C4×D4—36no—
664C4×D4—36no—
665C4×D4C22×D313yes—
666C4×D4C22×D313yes—
667C4×D4C22×D3112yes—
668#117—33no—
669#117—33no—
670#117—33no—
671#117—32no—
672#117—312no—
673#117—312no—
674#117—36no—
675#117—312no—
676#117—36no—
677#117—36no—
678#117—312no—
679#117C22×D313yes—
680#117C22×D316yes—
681C2×C4⋊C4—33no—
682C2×C4⋊C4—33no—
683C2×C4⋊C4—312no—
684C2×C4⋊C4C22×D316yes—
685C2×C4⋊C4C22×D316yes—
686C2×C22⋊C4—312no—
687C2×C22⋊C4—312no—
688C2×C22⋊C4—36no—
689C2×C22⋊C4—324no—
690C2×C42—33no—
691C2×C42—33no—
692C2×C42—33no—
693C2×C42—33no—
694C2×C42—33no—
695C2×C42—33no—
696C2×C42—312no—
697C2×C42—33no—
698C2×C42—33no—
699C2×C42—33no—
700C2×C42—33no—
701C2×C42—31no—
702C2×C42C22×D313yes—
703C23×C3C2513yes—
704C22×D3—26no—
705C22×D3—224no—
706C22×D3—26no—
707C22×D3—43no—
708C22×D3—412no—
709C22×D3—412no—
710C22×D3C25112yes—
711C22×D3C2513yes—
712C22×D3C2511yescharacteristic
713C3×Q8—212no—
714C3×Q8—24no—
715C3×Q8—412no—
716C3×Q8C2×#4114yescomplemented
717C3×D4C2×#41112yescomplemented
718C2×C3×C4—26no—
719C2×C3×C4—26no—
720C2×C3×C4—412no—
721C2×C3×C4C2×#41112yescomplemented
722C2×C3×C4C2513yes—
723C2×C3×C4C2513yes—
724C2×C3×C4C2514yes—
725C2×C3×C4C25112yes—
726C2×C3×C4C2511yescharacteristic
727C2×C3×C4C2513yes—
728C2×C3×C4C2511yescharacteristic
729C2×C3×C4C2511yescharacteristic
730#67—224no—
731#67—212no—
732C2×Dic3—26no—
733C2×Dic3—26no—
734C2×Dic3—43no—
735C2×Dic3C2511yescharacteristic
736C2×Dic3C2513yes—
737C2×Dic3C2511yescharacteristic
738C2×Dic3C2513yes—
739C2×Dic3C2514yes—
740C2×Dic3C2513yes—
741C2×Dic3C2511yescharacteristic
742D12—224no—
743D12—212no—
744D12—224no—
745D12—26no—
746D12—212no—
747D12—212no—
748D12—412no—
749D12—412no—
750D12—424no—
751D12—412no—
752C4×D3—26no—
753C4×D3—22no—
754C4×D3—26no—
755C4×D3—26no—
756C4×D3—26no—
757C4×D3—224no—
758C4×D3—26no—
759C4×D3—22no—
760C4×D3—26no—
761C4×D3—26no—
762C4×D3—224no—
763C4×D3—43no—
764C4×D3—43no—
765C4×D3—424no—
766C4×D3—412no—
767C4×D3H(5,𝔽2)14yescomplemented
768Dic6—24no—
769Dic6—26no—
770C24—33no—
771C24—312no—
772#41—624no—
773#41—64no—
774#41—616no—
775#41—612no—
776#41—612no—
777#41—624no—
778#41—1224no—
779#41—1224no—
780#41—1224no—
781#41—1212no—
782#41#23918yescomplemented
783C2×Q8—33no—
784C2×Q8—32no—
785C2×Q8—412no—
786C2×Q8—64no—
787C2×Q8C23×D312yes—
788C2×Q8C23×D316yes—
789C2×Q8C23×D3112yes—
790C2×Q8C23×D311yescharacteristic
791C2×D4—36no—
792C2×D4—312no—
793C2×D4—36no—
794C2×D4—312no—
795C2×D4—36no—
796C2×D4—33no—
797C2×D4—312no—
798C2×D4—36no—
799C2×D4—312no—
800C2×D4—312no—
801C2×D4—312no—
802C2×D4—324no—
803C2×D4—612no—
804C2×D4—648no—
805C2×D4—624no—
806C2×D4—1212no—
807C2×D4—1212no—
808C2×D4—1224no—
809C2×D4C23×D313yes—
810C22×C4—31no—
811C22×C4—33no—
812C22×C4—33no—
813C22×C4—33no—
814C22×C4—31no—
815C22×C4—31no—
816C22×C4—33no—
817C22×C4—33no—
818C22×C4—33no—
819C22×C4—33no—
820C22×C4—33no—
821C22×C4—33no—
822C22×C4—33no—
823C22×C4—312no—
824C22×C4—312no—
825C22×C4—33no—
826C22×C4—33no—
827C22×C4—312no—
828C22×C4—324no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—126no—
832C22×C4—1224no—
833C22×C4C23×D313yes—
834C22×C4C23×D313yes—
835C22×C4C23×D3112yes—
836C22×C4C23×D313yes—
837C4⋊C4—33no—
838C4⋊C4—312no—
839C4⋊C4—33no—
840C4⋊C4—36no—
841C4⋊C4—36no—
842C4⋊C4—32no—
843C4⋊C4—34no—
844C4⋊C4—34no—
845C4⋊C4—32no—
846C4⋊C4—312no—
847C4⋊C4C23×D3112yes—
848C4⋊C4C23×D313yes—
849C4⋊C4C23×D313yes—
850C4⋊C4C23×D316yes—
851C4⋊C4C23×D316yes—
852C4⋊C4C23×D3112yes—
853C4⋊C4C23×D312yes—
854C4⋊C4C23×D3112yes—
855C4⋊C4C23×D3112yes—
856C4⋊C4C23×D312yes—
857C22⋊C4—36no—
858C22⋊C4—312no—
859C22⋊C4—312no—
860C22⋊C4—324no—
861C22⋊C4—312no—
862C22⋊C4—36no—
863C22⋊C4—36no—
864C22⋊C4—324no—
865C22⋊C4—34no—
866C22⋊C4—312no—
867C22⋊C4—312no—
868C22⋊C4—312no—
869C22⋊C4—312no—
870C22⋊C4C23×D3112yes—
871C22⋊C4C23×D316yes—
872C42—31no—
873C42—33no—
874C42—31no—
875C42—31no—
876C42—33no—
877C42—33no—
878C42—34no—
879C42—33no—
880C42—33no—
881C42—33no—
882C42—33no—
883C42—33no—
884C42—33no—
885C42—312no—
886C42C23×D311yescharacteristic
887C42C23×D313yes—
888C42C23×D313yes—
889C42C23×D313yes—
890C42C23×D3112yes—
891C22×C3—23no—
892C22×C3—23no—
893C22×C3C22×#4116yes—
894C22×C3C2611yescharacteristic
895C2×D3—21no—
896C2×D3—21no—
897C2×D3—23no—
898C2×D3—212no—
899C2×D3—23no—
900C2×D3—212no—
901C2×D3—23no—
902C2×D3—212no—
903C2×D3—412no—
904C2×D3—824no—
905C2×D3C2×H(5,𝔽2)12yes—
906C3×C4—23no—
907C3×C4—212no—
908C3×C4—24no—
909C3×C4—23no—
910C3×C4C22×#4112yes—
911C3×C4C22×#4116yes—
912C3×C4C2×H(5,𝔽2)12yes—
913C3×C4#58512yes—
914Dic3—23no—
915Dic3—24no—
916Dic3—21no—
917Dic3—23no—
918Dic3—23no—
919Dic3—21no—
920Dic3C2×H(5,𝔽2)12yes—
921C23—31no—
922C23—312no—
923C23—33no—
924C23—66no—
925C23—66no—
926C23—624no—
927C23—123no—
928C23—1212no—
929C23—1212no—
930C23C24×D313yes—
931Q8—212no—
932Q8—24no—
933Q8—412no—
934Q8—66no—
935Q8—64no—
936Q8C2×#23914yescomplemented
937D4—624no—
938D4—624no—
939D4—612no—
940D4—624no—
941D4—612no—
942D4—66no—
943D4—612no—
944D4—612no—
945D4—1212no—
946D4—1224no—
947D4—1212no—
948D4—1212no—
949D4C2×#239112yescomplemented
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—31no—
953C2×C4—34no—
954C2×C4—31no—
955C2×C4—31no—
956C2×C4—33no—
957C2×C4—33no—
958C2×C4—34no—
959C2×C4—33no—
960C2×C4—412no—
961C2×C4—66no—
962C2×C4—624no—
963C2×C4—66no—
964C2×C4—66no—
965C2×C4—66no—
966C2×C4—62no—
967C2×C4—66no—
968C2×C4—66no—
969C2×C4—66no—
970C2×C4—624no—
971C2×C4—66no—
972C2×C4—62no—
973C2×C4—66no—
974C2×C4—1224no—
975C2×C4—123no—
976C2×C4—123no—
977C2×C4—1212no—
978C2×C4—123no—
979C2×C4C2×#239112yescomplemented
980C2×C4C24×D313yes—
981C2×C4C24×D313yes—
982C2×C4C24×D314yes—
983C2×C4C24×D3112yes—
984C2×C4C24×D311yescharacteristic
985C2×C4C24×D313yes—
986C2×C4C24×D311yescharacteristic
987C2×C4C24×D311yescharacteristic
988C2×C3—26no—
989C2×C3C23×#4111yescharacteristic
990C2×C3C22×H(5,𝔽2)11yescharacteristic
991C2×C3C2×#58511yescharacteristic
992D3—22no—
993D3—43no—
994D3—412no—
995C22—23no—
996C22—23no—
997C22—32no—
998C22—61no—
999C22—61no—
1000C22—63no—
1001C22—612no—
1002C22—63no—
1003C22—612no—
1004C22—63no—
1005C22—612no—
1006C22—1212no—
1007C22—2424no—
1008C22C22×#23916yes—
1009C22C25×D311yescharacteristic
1010C4—23no—
1011C4—212no—
1012C4—23no—
1013C4—24no—
1014C4—32no—
1015C4—61no—
1016C4—64no—
1017C4—63no—
1018C4—63no—
1019C4—61no—
1020C4—63no—
1021C4C22×#23916yes—
1022C4C22×#23912yes—
1023C4D3×H(5,𝔽2)12yes—
1024C4#596812yes—
1025C3#6280011yescharacteristic, complemented, Sylow
1026C2—26no—
1027C2—62no—
1028C2—123no—
1029C2—1212no—
1030C2C23×#23911yescharacteristic
1031C2C2×D3×H(5,𝔽2)11yescharacteristic
1032C2C2×#596811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3503C2
hypercenter#3503D3
hypocenterC3#62800
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3503

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#3503C2semidirect
2. #87043C2semidirect
3. #87040C2semidirect
4. #87023C2semidirect
5. #87016C2semidirect
6. #86933C2semidirect
7. #86924C2semidirect
8. #86748C2semidirect
9. D4×#239C2semidirect
10. #86597C2semidirect
11. #86582C2semidirect
12. #86261C2semidirect
13. #86257C2semidirect
14. #86205C2semidirect
15. C2×#5725C2semidirect
16. #85900C2semidirect
17. #85886C2semidirect
18. #85846C2semidirect
19. C4×D3×#41C2semidirect
23. C22×#239C22semidirect
24. C3×Q82C22semidirect
25. C3×#557C22semidirect
26. C3×#554C22semidirect
27. C3×D4×Q8C22semidirect
28. C3×#544C22semidirect
29. C3×#533C22semidirect
30. C2×C3×C4⋊Q8C22semidirect
34. #5817C22semidirect
35. C2×#947C22semidirect
36. #5734C22semidirect
37. #5734C22semidirect
38. #5733C22semidirect
39. #5733C22semidirect
40. #5732C22semidirect
41. #5730C22semidirect
42. #5728C22semidirect
43. #5728C22semidirect
44. #5726C22semidirect
45. #5726C22semidirect
46. #5725C22semidirect
47. #5725C22semidirect
48. #5725C22semidirect
49. #5725C22semidirect
50. #5725C22semidirect
51. #5725C22semidirect
52. #5725C22semidirect
53. #5725C22semidirect
54. #5725C22semidirect
55. #5725C22semidirect
56. #5697C22semidirect
57. #5697C22semidirect
58. #5695C22semidirect
59. #5695C22semidirect
60. #5691C22semidirect
61. #5691C22semidirect
62. #5691C22semidirect
63. #5644C22semidirect
64. #5637C22semidirect
65. #5630C22semidirect
66. #5630C22semidirect
67. #5630C22semidirect
68. #5627C22semidirect
69. #5627C22semidirect
70. #5627C22semidirect
71. #5624C22semidirect
72. #5624C22semidirect
73. #5585C22semidirect
74. #5585C22semidirect
75. #5580C22semidirect
76. #5580C22semidirect
77. #5577C22semidirect
78. #5577C22semidirect
79. #5577C22semidirect
80. #5577C22semidirect
81. #5577C22semidirect
82. #5576C22semidirect
83. #5574C22semidirect
84. C4×#239C22semidirect
85. C4×#239C22semidirect
86. C4×#239C22semidirect
87. C4×#239C22semidirect
88. C4×#239C22semidirect
89. C4×D3×Q8C22semidirect
90. C4×D3×Q8C22semidirect
91. #5554C22semidirect
92. D4×D12C22semidirect
93. D4×D12C22semidirect
94. D4×D12C22semidirect
95. #5545C22semidirect
96. C4×D3×D4C22semidirect
97. C4×D3×D4C22semidirect
98. C4×D3×D4C22semidirect
99. C4×#237C22semidirect
100. C4×#237C22semidirect
101. #5525C22semidirect
102. #5525C22semidirect
103. #5524C22semidirect
104. #5522C22semidirect
105. #5522C22semidirect
106. #5521C22semidirect
107. D3×#117C22semidirect
108. #5514C22semidirect
109. #5510C22semidirect
110. C2×#895C22semidirect
111. C2×#895C22semidirect
112. #5504C22semidirect
113. C2×#893C22semidirect
114. C2×#893C22semidirect
115. #5477C22semidirect
116. C2×#874C22semidirect
117. C4×#235C22semidirect
118. C2×C42×D3C22semidirect
125. #3503D3semidirect
316. Q82C2×D3semidirect
317. #557C2×D3semidirect
322. #554C2×D3semidirect
332. D4×Q8C2×D3semidirect
344. #544C2×D3semidirect
355. #533C2×D3semidirect
367. C2×C4⋊Q8C2×D3semidirect
411. C3×#41#41semidirect
716. C3×Q8C2×#41semidirect
717. C3×D4C2×#41semidirect
721. C2×C3×C4C2×#41semidirect
767. C4×D3H(5,𝔽2)semidirect
782. #41#239semidirect
936. Q8C2×#239semidirect
949. D4C2×#239semidirect
979. C2×C4C2×#239semidirect
1025. C3#62800semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#35032
#870432
#870402
#870232
#870162
#869332
#869242
#867482
D4×#2392
#865972
#865822
#862612
#862572
#862052
C2×#57252
#859002
#858862
#858462
C4×D3×#412
#628003